Question

You have 18 tuning forks that oscillate at close but different frequencies. What are the (a) maximum and (b) minimum number of different beat frequencies you can produce by sounding the forks 2 at a time, depending on how the frequencies differ?

Answer 1

The maximum number of different beat frequencies that 18 tuning forks can produce is 153, while the minimum number is 1, depending on the uniqueness of each fork's frequency.

Step-by-step explanation:

To determine the number of different beat frequencies produced by 18 tuning forks, we need to consider the concept of beating, which occurs when two sound waves of slightly different frequencies interfere with each other. The beat frequency is equal to the absolute difference between the two frequencies.

(a) The maximum number of different beat frequencies occurs when each fork has a unique frequency, different from all others. Since each pair of forks can produce a unique beat frequency, we use a combination formula to find the number of possible pairs: C(18, 2) which is 18! / (2!(18 - 2)!) = 153.

(b) The minimum number of different beat frequencies would be observed if all forks had frequencies that were sequential or if pairs had the same frequency. This would result in only one beat frequency, so the minimum number is 1.